WASHINGTON (CNN) -- The charge that Saudi Arabia made a secret pact with President Bush to lower gasoline prices in time to help him in the November presidential election was denied Monday by the White House, the Saudi ambassador to the United States -- and even by journalist Bob Woodward, who raised the specter of such a quid pro quo in a book released Monday.

"I don't say there's a secret deal or any collaboration on this," Woodward told CNN's "Larry King Live" Monday. "What I say in the book is that the Saudis ... hoped to keep oil prices low during the period before the election, because of its impact on the economy. That's what I say."

The Saudi ambassador to the United States, Prince Bandar bin Sultan, who appeared on the program with Woodward, said his characterization of Saudi policy was "accurate."

"We hoped that the oil prices will stay low, because that's good for America's economy, but more important, it's good for our economy and the international economy," he said. "This is nothing unusual. President Clinton asked us to keep the prices down in the year 2000. In fact, I can go back to 1979, President Carter asked us to keep the prices down to avoid the malaise."

"So yes, it's in our interests and in America's interests to keep the prices down. But that was not a deal."

Bandar said much the same thing on April 1, after he met with national security adviser Condoleezza Rice at the White House amid concerns that OPEC production cuts might further push up the price of oil, with U.S. gas prices already at record levels.

Bandar said then that the Saudis wanted to keep the per-barrel price of oil, now topping $33, to between $22 and $28 a barrel, and he also said Bush and Crown Prince Abdullah, Saudi Arabia's de facto ruler, "have been in touch on this subject for a while now."

"Saudi Arabia does not live on the moon. When the world economy gets hurt, we get hurt also," Bandar said.

The ambassador, a longtime friend of the Bush family, was asked by King Monday if he wanted to see Bush re-elected.

"We always want any president who is in office to be re-elected, Larry, but that is the American choice. This is not our call. This is the American people's call," Bandar said.

Woodward's suggestion in an interview Sunday on CBS's "60 Minutes" that the Saudis might be trying to tinker with oil prices to help Bush politically raised a firestorm Monday, with presumptive Democratic presidential nominee Sen. John Kerry leading the charge.

"If, as Bob Woodward reports, it is true that gas supplies and prices in America are tied to the American election, then tied to a secret White House deal, that is outrageous and unacceptable to the American people," he said during a campaign stop in Florida.

"It is fundamentally wrong," he said. "It's my prayer that Americans are not being held hostage to a secret deal."

Asked by King about Kerry's reaction, Woodward said, "Kerry has taken this to the next level. This always gets caught in the political crossfire, and I'm trying to stick with what my reporting showed."

The three top Democrats in the House, Minority Leader Nancy Pelosi of California, Minority Whip Steny Hoyer of Maryland and Democratic Caucus Chair Bob Menendez of New Jersey, sent a letter to the White House demanding that Bush "fully explain the agreement that you or your administration reached with the Saudis to boost oil production and disclose any promises or commitments that have been made to the Saudis on behalf of the U.S."

In his book, "Plan of Attack," Woodward reported that prior to the invasion of Iraq, Bandar was briefed on top-secret U.S. war plans in order to enlist Saudi support. He also met with Bush at the White House.

White House Communications Director Dan Bartlett told CNN's "Inside Politics" that Bush and Bandar discussed the possibility that military conflict in Iraq would lead to "a major disruption of oil supplies across the globe, particularly hurting Americans here at home."

"What we were reassured by was the fact that Saudi Arabia was not going to allow that to happen, was going to work with other OPEC members to make sure there was not an emergency spike in prices," he said.

Asked whether Woodward's reporting was wrong, Bartlett said, "I'm saying what Prince Bandar said was the long-term oil strategy for Saudi Arabia is the same that they've been publicly stating. There would be an oil price per barrel of $22 to $28. There was no secret deal."